On the Existence of Equilibrium in Bayesian Games Without Complementarities

Idione Meneghel and Rabee Tourky
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Idione Meneghel: Australian National University College of Business and Economics, https://cbe.anu.edu.au/welcome-cbe
Rabee Tourky: Australian National University College of Business and Economics, https://cbe.anu.edu.au/welcome-cbe

No 2190, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: In a recent paper, Reny (2011) generalized the results of Athey (2001) and McAdams (2003) on the existence of monotone strategy equilibrium in Bayesian games. Though the generalization is subtle, Reny introduces far-reaching new techniques applying the fixed point theorem of Eilenberg and Montgomery (1946, Theorem 5). This is done by showing that with atomless type spaces the set of monotone functions is an absolute retract and when the values of the best response correspondence are non-empty sub-semilattices of monotone functions, they too are absolute retracts. In this paper, we provide an extensive generalization of Reny (2011), McAdams (2003), and Athey (2001). We study the problem of existence of Bayesian equilibrium in pure strategies for a given partially ordered compact subset of strategies. The ordering need not be a semilattice and these strategies need not be monotone. The main innovation is the interplay between the homotopy structures of the order complexes that are the subject of the celebrated work of Quillen (1978), and the hulling of partially ordered sets, an innovation that extends the properties of Reny's semilattices to the non-lattice setting. We then describe some auctions that illustrate how this framework can be applied to generalize the existing results and extend the class of models for which we can establish existence of equilibrium. As with Reny (2011), our proof utilizes the fixed point theorem in Eilenberg and Montgomery (1946).

Keywords: Bayesian games; Monotone strategies; Pure-strategy equilibrium; Auctions (search for similar items in EconPapers)
JEL-codes: C72 D44 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2019-08
New Economics Papers: this item is included in nep-des, nep-gth and nep-mic
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